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Communications on Pure and Applied Analysis (CPAA)
 

Orbital stability of solitary waves of the Schrödinger-Boussinesq equation

Pages: 1043 - 1050, Volume 6, Issue 4, December 2007      doi:10.3934/cpaa.2007.6.1043

 
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Sevdzhan Hakkaev - Faculty of Mathematics and Informatics, Shumen University, 9712 Shumen, Bulgaria (email)

Abstract: This paper concerns the orbital stability of solitary waves of the Schrödinger-Boussinesq equation

$ i\partial_t u+\partial_x^2 u+uv =0\qquad\qquad\qquad\qquad\qquad (0.1)$

$ \partial_t^2 v-\partial_x^2 v+\partial_x^4 v+\partial_x^2 (3v^2+|u|^2)=0.$

By applying the abstract results of Grillakis, Shatah and Strauss [11, 12] and detailed spectral analysis developed by Lopes in [17], we obtain the stability of solitary waves.

Keywords:  Solitary wave, stability, Schrödinger-Boussinesq equation.
Mathematics Subject Classification:  35Q55, 35B35, 37K45.

Received: February 2007;      Revised: July 2007;      Available Online: September 2007.